Simplify the following expression and state the condition under which the simplification is valid. $z = \dfrac{n^2 - 9}{n + 3}$
First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = n$ $ b = \sqrt{9} = 3$ So we can rewrite the expression as: $z = \dfrac{({n} + {3})({n} {-3})} {n + 3} $ We can divide the numerator and denominator by $(n + 3)$ on condition that $n \neq -3$ Therefore $z = n - 3; n \neq -3$